Acoustic logging is accomplished with acoustic transmitters and receivers in a sonde. The sonde is lowered in a borehole on a logging cable. Typically two acoustic receiver transducer elements are located in the sonde. Heretofore, acoustic transducer elements have been constructed constrained by with the surrounding structure (the cylindrical sonde), thereby being confined by the shape of the sonde. One typical device which has found favor in the past is a right cylinder transducer. This right cylinder construction has met with great favor in the past. Typically, they are formed of transducer material for operating as a piezoelectric crystal to transmit and receive acoustic signals. One suitable material is lead titanate zirconate. This provides a relatively successful acoustic receiver.
Cylindrical transducer elements exhibit mechanical resonant frequencies. These frequencies are dependent on the geometric construction of the device. For a hollow right cylinder, there are three modes of mechanical resonance, one being dependent on the wall thickness, another being dependent on the length of the right cylinder, and another being dependent on the diameter of the cylinder. Consider as an example a hollow right cylinder made of the above referenced material operating as an acoustic transducer. If the wall thickness is 0.15 inches, the resonant frequency is given by 75/t kHz, or with this thickness, a frequency of about 493 kHz. That is sufficiently high that it poses no problem. Consider such a cylinder which is one inch in length. There is a resonance along the length also. The resonant frequency in this relationship is given by 59/L kHz, or 59 kHz when the length is one inch. This is markedly lower than 493 kHz mentioned above; it is still sufficiently high that it is reasonably out of the range at which it can pose a problem.
If the cylinder has a diameter of 2.5 inches, the radial mode resonance is given by the relationship of 38/d kHz or 14.3 kHz with this diameter. Decreasing the diameter may increase the resonant frequency; that may be desirable but only at a cost. The cost is reduction of power capacity of the smaller transducer. Moreover, if the sonde is able to accommodate a crystal of about 2.5 inches diameter, it is highly desirable that the largest permissible crystal be installed to obtain reasonable coupling to the crystal. Regretably, this is accomplished only at the cost of having a mechanical resonant frequency of 14.3 kHz, a peak which is well within the typical band width of an acoustic receiver.
An acoustic receiver preferably operates with a band width of about 25 kHz frequency, typically between about 1.0 and 25.0 kHz. The radial mode resonance frequency peak is undesirable because it falls in the middle of this band and distorts the gain across the band. The useful data normally is found within a band of about one to about 25 kHz. Because this is true, the resonant frequency of the structure used as the transducer is ideally located outside the band width of the receiving device.
It has been discovered that a cone shaped transducer has resonant frequency points which are higher. Through the use of a hollow cone shaped transducer base structure, resonant frequency points are above 25 kHz and pose no problem. Such a structure does not have resonant frequency points below 25 kHz. For instance, utilizing an aluminum substrate, a cone shaped transducer has been constructed and tested. Such a structure has fifteen sides. The sides are planar surfaces constructed with trapezoidal faces. Suitable transducer crystals are attached by conductive adhesives to the respective trapezoidal faces. It is possible to utilize such a device to form an acoustic transducer having a passband of about one kHz to about 25 kHz wherein the mechanical resonant points are above the desired passband.